{
  "id": "1402.7303",
  "version": "v2",
  "published": "2014-02-28T16:21:21.000Z",
  "updated": "2014-06-13T17:32:21.000Z",
  "title": "The Non-Commutative Geometry of the Complex Classes of Topological Insulators",
  "authors": [
    "Emil Prodan"
  ],
  "comment": "Final version",
  "journal": "Topol. Quantum Matter 1, 1-16 (2014)",
  "doi": "10.2478/topor-2014-0001",
  "categories": [
    "math-ph",
    "cond-mat.dis-nn",
    "math.MP",
    "math.OA"
  ],
  "abstract": "Alain Connes' Non-Commutative Geometry program [Connes 1994] has been recently carried out [Prodan, Leung, Bellissard 2013, Prodan, Schulz-Baldes 2014] for the entire A- and AIII-symmetry classes of topological insulators, in the regime of strong disorder where the insulating gap is completely filled with dense localized spectrum. This is a short overview of these results, whose goal is to highlight the methods of Non-Commutative Geometry involved in these studies. The exposition proceeds gradually through the cyclic cohomology, quantized calculus with Fredholm-modules, local formulas for the odd and even Chern characters and index theorems for the odd and even Chern numbers. The characterization of the A- and AIII-symmetry classes in the presence of strong disorder and magnetic fields emerges as a natural application of these tools.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-13T17:32:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological insulators",
      "complex classes",
      "aiii-symmetry classes",
      "strong disorder",
      "magnetic fields emerges"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.7303P"
    }
  }
}